Everton refused to settle for a tie even though they were on track to do so against West Ham, as the two teams each had one goal after regulation time ended.
Three minutes of stoppage time were added to the clock, and Everton striker Romelu Lukaku took advantage of that by scoring the winning goal 92 minutes into the match.
This made for an exciting finish after the first half was completely uneventful, as neither team scored a goal or committed any major penalty.
Everton did have two yellow cards thrown their way in the first half, and West Ham received one.
In the second half, West Ham took a 1-0 lead 62 minutes into the game with a goal from forward Stewart Downing.
Everton responded quickly with a game-tying goal from midfielder Leon Osman, who roundhouse kicked the ball into the right side of the goal.
Lukaku saved the best moment of the game for last though, as he came through in the clutch for Everton with the game-winning goal.
This marks six games that he has played against West Ham since joining Everton, and the 22-year-old striker has scored one goal in each of those games.
Everton is now in 10th place with 47 points, and they hold the tiebreaker over West Ham, who has dropped to 11th place.